Why you should never exercise American options?

Posted in Uncategorized by qmarks on November 22, 2010

Actually a better question is, why you shouldn’t early exercise your american call option? Early exercising American call option on a non dividend paying stock is not optimal for two reasons. One delaying exercise delays the payement of the strike price. This means that the option holder is able to earn interest on the strike price for a longer period of time.

Second assume that you exercised your option today, what if tomorrow a big crazy thing will occur and the price of an underlying asset just shoots? Sorry baby you already exercised your option and you sold your right to buy at a very cheap price. Instead of exercising your American call option you should have sold it to someone else.

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This is not entirely correct. Using your words “If tomorrow a big crazy thing occur and price of an underlying bottoms down”. What do you do?

All the theory in books is concerned with Risk Neutral World, which is like believing in Santa Claus ;). As a speculator if you know tomorrow stock might follow u do exercise. The decision not to exercise is written in terms of option seller who is hedging & not the buyer who in most cases is just speculating.

Thank you very much for your feedback Quantanalysis. I will try to convince you why you should never exercise your American call option early.

When you buy option, call or put, you buy the volatility. Thus you should be interested in the direction of volatility instead of price.
Second the beauty behind the Black-Scholes is the ability to set-up a risk-free portfolio, which allows you to speculate either direction, the value of your portfolio at a future time can be discounted by a risk free rate. The option price you see is calculated through this Risk Neutral World rate.

The answer to the question, why you should never early exercise call option goes like this. Suppose today you are considering exercising early an in-the-money American call option. If you exercise you pay the Strike price and receive an asset worth of Spot. If that was a European Call option, you did not have the right to exercise early, and the option worth at least Spot- Strike/ (1+ rate)^time, [Spot – Strike (discounted)] or underlying price minus the present value of the exercise price which is greater than Spot less Strike. You should already know that the the American call must be worth no less than the European call, it therefore must also be worth at least Spot – Strike(discounted). this means the value you can obtain by selling it to someone else is more than the value you can obtain by exercising it. Thus there is no reason to exercise the call early. Put it this way, exercising a call eraly simply gives the money to the call writer and throws away the speculator’s right to decide whether you want the underlying asset or not.

I understand this theory. My point is a bit different. Let me clarify.
Black Scholes is nice, but doesn’t work in Incomplete Markets. All the hedging theory works in complete markets and this includes optimal exercise time for American option.

Consider a very crude example, I buy an option from Goldman Sachs (as their client). After 7 days my speculating view is I don’t want to hold that option. The option had the american exercising feature, but the problem is it’s hard to sell. Why? Coz it was customized for me, so it’s not easy to sell. Would you exercise it to get out of this position?

I am only speculating, I don’t want to hedge. What do you do in this case?
It’s actually a controversial topic still in academics!

Another thing I find weird with many books on Risk Neutral world is
“A replicating portfolio for derivatives….and etc…”.
If you can replicate everything why actually buy derivatives……..
Since you can replicate….it will make derivatives redundant…and hence the book redundant!

I am only speculating, I don’t want to hedge, what do you do in this case?

I am not sure what do you do in this case, I guess that’s one of the assumption in the model, you know the “theoretical world”.

Answer to second comment is, if you replicate the portfolio through many assets, why should you pay commission twice, when you can hold the derivative itself. Say, put-call parity. People buy the stock and the put , but actually replicate a portfolio with a call and fixed income security. Then just hold the call option. That’s my two cents. If you have a better reasoning, please share.